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    On the Stability of the Finite Difference based Lattice Boltzmann Method

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    Type
    Conference Paper
    Authors
    El-Amin, Mohamed cc
    Sun, Shuyu cc
    Salama, Amgad cc
    KAUST Department
    Computational Transport Phenomena Lab
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Earth Science and Engineering Program
    Physical Science and Engineering (PSE) Division
    Date
    2013-06-01
    Online Publication Date
    2013-06-01
    Print Publication Date
    2013
    Permanent link to this record
    http://hdl.handle.net/10754/552433
    
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    Abstract
    This paper is devoted to determining the stability conditions for the finite difference based lattice Boltzmann method (FDLBM). In the current scheme, the 9-bit two-dimensional (D2Q9) model is used and the collision term of the Bhatnagar- Gross-Krook (BGK) is treated implicitly. The implicitness of the numerical scheme is removed by introducing a new distribution function different from that being used. Therefore, a new explicit finite-difference lattice Boltzmann method is obtained. Stability analysis of the resulted explicit scheme is done using Fourier expansion. Then, stability conditions in terms of time and spatial steps, relaxation time and explicitly-implicitly parameter are determined by calculating the eigenvalues of the given difference system. The determined conditions give the ranges of the parameters that have stable solutions.
    Citation
    On the Stability of the Finite Difference based Lattice Boltzmann Method 2013, 18:2101 Procedia Computer Science
    Publisher
    Elsevier BV
    Journal
    Procedia Computer Science
    Conference/Event name
    13th Annual International Conference on Computational Science, ICCS 2013
    DOI
    10.1016/j.procs.2013.05.380
    Additional Links
    http://linkinghub.elsevier.com/retrieve/pii/S1877050913005231
    ae974a485f413a2113503eed53cd6c53
    10.1016/j.procs.2013.05.380
    Scopus Count
    Collections
    Conference Papers; Physical Science and Engineering (PSE) Division; Earth Science and Engineering Program; Computational Transport Phenomena Lab; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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